Pith Number

pith:W53MS4OH

pith:2012:W53MS4OH2KRBFUHYFVFA6VHDAJ

not attested not anchored not stored refs pending

Squirals and beyond: Substitution tilings with singular continuous spectrum

Michael Baake (Bielefeld), Uwe Grimm (Milton Keynes)

arxiv:1205.1384 v1 · 2012-05-07 · math.DS · math.MG

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{W53MS4OH2KRBFUHYFVFA6VHDAJ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-17T23:53:18.750202Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

b776c971c7d2a212d0f82d4a0f54e3025fae32b7ac650d3f3b1b717439188dc4

Aliases

arxiv: 1205.1384 · arxiv_version: 1205.1384v1 · doi: 10.48550/arxiv.1205.1384 · pith_short_12: W53MS4OH2KRB · pith_short_16: W53MS4OH2KRBFUHY · pith_short_8: W53MS4OH

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/W53MS4OH2KRBFUHYFVFA6VHDAJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: b776c971c7d2a212d0f82d4a0f54e3025fae32b7ac650d3f3b1b717439188dc4

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "7f0f6002db3d05c05f23599628bfe68384d2e6bfe0fc4de3d20013e1a453c9f3",
    "cross_cats_sorted": [
      "math.MG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.DS",
    "submitted_at": "2012-05-07T13:40:38Z",
    "title_canon_sha256": "e2a6cce9dd77eccb6bc64e3f93064603b3e2ab58703e1e74eaa77b2be7012d3e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1205.1384",
    "kind": "arxiv",
    "version": 1
  }
}